On the relativistic impulse approximation for the calculation of Compton scattering cross sections and photon interaction coefficients used in kV dosimetry

We calculate differential and integrated cross sections for the Compton interaction as well as mass

attenuation (μC/ρ), mass energy-transfer (μC

tr/ρ), and mass energy-absorption (μen/ρ)

coefficients, within the relativistic impulse approximation (RIA) using Compton profiles (CPs)

obtained from unrestricted Hartree–Fock electron densities. We investigate the impact of using

molecular as opposed to atomic CPs on dosimetric photon interaction coefficients for air, water

and graphite, and compare our cross sections to the simpler Waller–Hartree (WH) and

Klein–Nishina (KN) formalisms. We find that differences in μC/ρ and μC

tr/ρ resulting from the

choice of CPs within the RIA are small relative to the differences between the RIA, WH, and KN

calculations. Surprisingly, although the WH binding corrections seem accurate when considering

μC/ρ, there are significant discrepancies between the WH and RIA results when we look at μC

tr/ρ.

The WH theory can differ substantially from the predictions of KN and the RIA in the tens of keV

range (e.g. 6%–10% at 20 keV), when Compton scattering becomes the dominant interaction

mechanism. For lower energies, the disagreement further grows to about one order of magnitude

at 1 keV. However, since the photoelectric effect transfers more energy than the Compton

interaction in the tens of keV range and below, the differences in the total μen/ρ values resulting

from the choice of Compton models (KN, WH, or RIA) are not larger than 0.4%, and the

differences between WH and the other two theories are no longer prominent.